When Heat's editor-in-chief Lucie Cave appeared before the Leveson inquiry, the live video stream showed Lord Justice Leveson with the magazine laid out in front of him, opened at its regular double-page spread, "Who's doing who? (because celebs' love lives are even more bonkers than ours!)".

"It was quite daunting because it was just the three of us, representing every magazine. I told it like it was, that the whole Leveson investigation had come about because of phone hacking and it wasn't anything that we as magazines had been a part of."

But Heat is not as hot as it was. The byword for celebrity gossip for much of the last decade, selling more than 700,000 copies at its peak, its average weekly sale slipped to 261,715 in the second half of last year. "We have been holding steady," says Cave. Not quite, down nearly 10% on the first half of 2012 and nearly 20% year on year.

Still, it can't be easy up against the showbiz behemoth that is the Daily Mail's website, Mail Online (which had 111 million users last month) and its infamous "sidebar of shame" featuring celebrities in various states of undress and disgrace. "It's there, I'm not frightened by it," says Cave. "The Daily Mail is very negative, they just churn stuff out and will cover literally everything. We are more selective. There is still a real role to play for a brand like Heat which is much more personality-led and there to make people laugh."

At its height Heat is estimated to have made profits of around £9m a year (launched by Emap, it is now part of privately-owned German media company, Bauer). Bauer does not talk numbers, but industry sources say it now makes around £2m.

A presenter on the (now defunct) teen TV channel Trouble before joining Heat in 2003, Cave knew its then editor Mark Frith, having done work experience for him while he was editing Smash Hits. It was Frith who turned Heat around after its disastrous £4m launch in 1999 as a sort of UK equivalent of Entertainment Weekly. It failed to find an audience and was weeks away from closure before it was reinvented as a celebrity gossip title.

Regular features include "Spotted" in which readers are offered £200 for an unposed picture of a celebrity. Ten years ago, Ewan McGregor called Heat a "dirty, filthy piece of shit" over its use of paparazzi pictures. Cave says it still uses paparazzi photos but would never use them out of context or of someone who was "clearly distressed or had been harassed".

She told Leveson that she would support a register of celebrities who didn't want their pictures taken, but now admits it would be impractical. "I don't believe that celebrities are public property. They play the game – some of them more than others – but I don't believe that people should be followed around because they are a celebrity," she says.

"When we meet them they love the spirit of the magazine, they know we are not there to be mean-spirited. We are there to entertain and if they embrace that … it's going to make them look better."

Declining circulation figures can often precipitate a title's plunge downmarket but Cave, appointed editor in 2011 and editor-in-chief last year, says the reverse has been true. Innovations such as the "circle of shame" and the "hoop of horror" – pointing out an unfortunate sweat patch, wardrobe malfunction or worse – were ditched long ago. "If you had a bit of tit tape hanging out of your bra it would point that out. It made them seem a bit more real but … we play it a bit more responsibly now. It's about being cheeky and funny, not mean."

The magazine was never meaner than in 2007 when it printed a sticker of Katie Price's disabled son, Harvey, captioned "Harvey wants to eat me". The publication later apologised and made a donation to charity. Cave told the Leveson inquiry: "It was a grave mistake. Everyone who works for the magazine at the time and still works for the magazine is mortified by that incident."

Heat has also been criticised for the way it treats celebrities' bodies and suggesting they are too thin – or too fat. "That's quite a long time ago," argues Cave. "We are really careful how we approach that because it's a delicate issue. But ultimately if there's a picture of a celebrity in a bikini there will still be women readers who are interested because they compare it to their bodies. If you hear a group of women talking, that's what they do."

As editor-in-chief – Jeremy Mark is editor – Cave oversees its other platforms which include the Heat TV channel launched last year, Heat Radio, and its website, Heat World. Heat Radio, which had 767,000 listeners in the final three months of last year, previously suffered from a lack of investment and was based in Manchester. Now it has a studio in Heat's London office in Shaftesbury Avenue.

"We have got all these brand extensions but they were working in silos a little bit," says Cave. Such is her enthusiasm for "Heat 360" that staff joke they should have it tattooed on their arms. "OK, it's extra work for them to do but they're embracing it. It's liberating for us," she adds.

The magazine is to relaunch its "Heat extra" app, featuring video and quizzes you can access when you point your phone at the latest issue. Heat's live coverage of the red carpet from the National Television Awards in January had around 15,000 viewers online. It also launched its first "Twitter awards" last week, with categories including "lifetime achievement award for services to Twitter" (Twitter is seven years old).

But it is tough for a weekly magazine like Heat to keep pace with social media, with celebrities using Twitter to talk direct to their followers (in Heat staple Rihanna's case, all 29 million of them). "We go to press on a Friday night and come out on a Tuesday. That is frustrating for a magazine like Heat," admits Cave.

Kim Kardashian is another Heat regular, but there are no guaranteed top-selling cover stars any more, says Cave, not even Victoria Beckham. In its heyday, Big Brother provided Heat with a succession of stars, none bigger than Jade Goody, with whom Cave collaborated as the ghost writer of her autobiography (she also wrote short-lived boyband Busted's 2004 "unofficial annual"). The decline of the show's ratings, now on Channel 5, mirrors Heat's circulation.

Appropriately for the editor of a weekly which has made a fortune from celebrity relationships, Cave is in one of her own, dating Ben Lunt, a former winner of Channel 4's reality show Shipwrecked.

"I interviewed him but it was about a year later he started asking me out," she explains. "He's a builder, he's gone back to his roots. He's not after fame." Although he did experience his 15 minutes – possibly less – as Heat's "torso of the week".

Cave says her most memorable moment on the magazine was persuading James Corden to pose, David Beckham-style, in his underpants ("vintage Heat") in 2008. She also highlights, in an email after our interview, the first interview with Imogen Thomas, alleged to have had an affair with footballer Ryan Giggs, and a series of pictures of celebrities without make-up or airbrushing.

The Duke and Duchess of Cambridge briefly became the centre of Heat's universe – Pippa Middleton ("P-middy") made the cover – but the glow has faded.

What about the Sun's naked pictures of Prince Harry? "I quite admire the Sun for putting it on the cover. There was frustration … but the Sun operates in a totally different world to Heat. We would never have done that," says Cave.

"The closest we would have gone was to get David Walliams to recreate the shot for our Christmas issue, which nearly happened." Walliams posing as Prince Harry? Without any clothes on? Now that really would have been vintage Heat.